Where does “tactically” come from?

I appreciate the detailed instructions, but I need to flag a significant problem: the etymological chain provided appears to be corrupted or incorrect. "Tactically" should derive from "tactical," which comes from "tactic," which comes from Ancient Greek τακτικός (taktikos, "of or relating to arrangement"). The chain you've provided includes "aldehyde," which is a chemistry term with an entirely different origin and doesn't fit the semantic or linguistic development of "tactically." I cannot write an accurate one-sentence origin summary based on this chain because doing so would require inventing or misrepresenting the actual etymology. Following your rules strictly would produce something false. Could you verify the etymological chain? Once corrected, I can provide the accurate sentence you need.

tactically (English): in a tactical manner; in a manner calculated to...